# Is it possible to create a specific wavelength

1. Feb 16, 2015

### Oliver McIrwin

I am wondering if a particular wavelength could be generated by Focusing two different wavelength lasers at the same spot? My hypothesis is no, because interference only affects amplitude and not wavelength,correct? Could there be another way of generating a specific wavelength from two dissimilar wavelengths? or any other method?

2. Feb 16, 2015

### Staff: Mentor

What do you mean by "a particular wavelength"? Do you mean pure monochromatic light of that wavelength? If so, obviously you can't make it from anything that has other wavelengths present. (See below for further comments.)

No. The waveform created by interference of monochromatic waves of different wavelengths will not be a monochromatic wave; that means it does not have a single well-defined "wavelength".

3. Feb 17, 2015

### Oliver McIrwin

I suppose the light wouldn't have to be monochromatic, it would need carry the desired wavelength at the point of intersection and ideally at no other point along its travel. Could that be possible by directing two laser beams of any wavelength other than my desired wavelength toward each other? Why or why not?

4. Feb 17, 2015

### Staff: Mentor

Wavelength is not something that has meaning at a single point; it only has meaning over enough of a distance to see crests and troughs of the wave.

The only way to have pure monochromatic light is to have pure monochromatic light; that is, a beam with a single wavelength. As I said before, if you interfere two beams with different wavelengths, the resulting light does not have a well-defined wavelength at all.

5. Feb 17, 2015

### blue_leaf77

If the two lasers are focused onto a nonlinear material then yes you can generate new frequency under phase matched condition.

6. Feb 17, 2015

### sophiecentaur

The theory behind this is straightforward and predictable - but the numbers (distances, frequencies) involved are important to what you could see. You do not need a non linearity to detect a beat between two signals when Interference in space will do it for you. The two signals have no effect on each other.
This sort of thing is observable all the time at lower (Radio) frequencies. the interference pattern from two transmissions with a small frequency (wavelength) difference can be observed to sweep across the 'mush area' between the two transmitters, producing a beat (at a fixed receiver) that may be at an audio rate or even slower. The practicalities of producing a similar effect with two lasers may be a bit harder to achieve but a moving 'standing' wave pattern could be produced if the two laser wavelengths were close enough. I'd bet it has been done.

7. Feb 17, 2015

### blue_leaf77

Well yeah as long as what one is interested in is the mere beat note. But in general one can't say the beat note as a true wavelength, since this beat note will form sinusoidal envelope only for two different interfering wavelengths. In more general case where there are more than two wavelengths, the beat note will not be sinusoidal anymore.
Besides, if you put spectrometer in the focus, there will be only two wavelengths observed.

8. Feb 17, 2015

### sophiecentaur

This is true. You hear a beat frequency. When an interference pattern is set up, there will be maxes and mins and the (what could be called the) spatial wavelength of the pattern will be the distance between maxes (fringe width) and not a new EM wave. The speed could be anything from zero to very high and the temporal beat frequency will be the speed/'wavelength'
This is also true but, when measuring the amplitude of the signal admitted into a wide band detector, you will still get a beat. This is exactly the same sort of thing as what you get with a spectrum analyser, displaying a simple Amplitude Mod of a carrier with a sine wave. You can observe three distinct, continuous frequencies or an AM signal, depending on the bandwidth setting.

9. Feb 26, 2015

### tech99

10. Feb 26, 2015

### tech99

If beats occurred between radio transmissions without the use of a on linear device, the radio spectrum would be filled with mixing products, which it is not. The two monochromatic light beams, if applied to a non linear device, will in principle produce monochromatic sum and difference frequencies. Of course, nothing is perfect, so we would expect to see a number of other mixing products and lower amplitude.

11. Feb 26, 2015

### sophiecentaur

I think you are confusing two things here. If you take two signals at frequency f1 and f2 and add them then the result is the sum of the phasors and its amplitude will change in time. If you put the two signals into a non linear circuit element then you can expect sum and difference products (as you say). That is what happens only when superposition does not apply and it is not what I am describing
In a linear system of waves of the same frequency, you could take a perfectly linear, resistive element - attached to a receiving antenna and the standing wave / interference pattern would show up as a variation in temperature of the resistive element with spatial position. Not a very sensitive method, I agree, but the temperature variation with position would be there, coinciding with the interference pattern. If you change the frequency of one of the signals then the interference would no longer be stationary. This detector, left in a fixed position, would produce a varying temperature, corresponding to the rate that the maxes and mins sweep past it. You would get a 'beat'. But the frequency of that beat will not be at f2-f1 it would be at a frequency depending on the ever-changing phase relationship between the two signals and the path difference between the signals to the reception point. This beat, often at a 'fluttering' frequency, is a very common occurrence between RF stations and is nothing to do with non linearity. It happens, for instance, when a skywave path is changing (Inospoheric layers altering in height and producing a doppler shift in the skywave signal) and the ground wave path remains constant. This is often referred to as the skywave mush area)
The effect can be detected with a normal radio receiver (much more sensitive) and, if the receiver has poor linearity, you will get both kinds of beat - the frequency mixing and the geometric effect - producing entirely different beat frequencies.